Modeling subpopulations for hierarchically structured data

Abstract

The field of forensic statistics offers a unique hierarchical data structure in which a population is composed of several subpopulations of sources and a sample is collected from each source. This subpopulation structure creates an additional layer of complexity. Hence, the data has a hierarchical structure in addition to the existence of underlying subpopulations. Finite mixtures are known for modeling heterogeneity; however, previous parameter estimation procedures assume that the data is generated through a simple random sampling process. We propose using a semi-supervised mixture modeling approach to model the subpopulation structure which leverages the fact that we know the collection of samples came from the same source, yet an unknown subpopulation. A simulation study and a real data analysis based on famous glass datasets and a keystroke dynamic typing data set show that the proposed approach performs better than other approaches that have been used previously in practice.